Question: $f(x)=6x-4$ $g(x)=3x^2-2x-10$ Write $(g\circ f)(x)$ as an expression in terms of $x$. $(g\circ f)(x)=$
Solution: First, let's write $(g\circ f)(x)$ as $g(f(x))$. Next we write $f(x)$ as the input to function $g$. $g({f(x)})=3({f(x)})^2-2({f(x)})-10$ Since $f(x)=6x-4$, this becomes: $\begin{aligned} g({f(x)})&=3({6x-4})^2-2({6x-4})-10\\ \\ &=3(36x^2-48x+16)-12x+8-10\\ \\ &=108x^2-144x+48-12x-2\\ \\ &=108x^2-156x+46 \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(g\circ f)(x)=108x^2-156x+46$